where \(\epsilon \in \mathbb {R}\)  is the inlier-outlier threshold and \(\phi (\mathcal {I}, \mathbf {p}) = \min _{h \in \mathcal {I}} \phi (h, \mathbf {p})\)  is the minimal point-to-model residual of point \(\mathbf {p}\)  given the kept set of dominant model instances \(\mathcal {I}\) .
In order to use the recent advances of RANSAC, the loss function of MAGSAC++ [1]} the currently most accurate method according to a recent survey [2]}, \(Q_{\text{RSC}}\)  is reformulated considering a continuous loss function \(f\) .
For practical considerations, we consider losses returning a value in-between 0 and 1. The quality function that \(f\)  implies is
\(Q_{f}(h, \mathcal {P}, \epsilon ) =|\mathcal {P}| - \sum _{\mathbf {p}\in \mathcal {P}} \max \left( f(h, \mathbf {p}), 1 - f(\mathcal {I}, \mathbf {p}) \right),\) 
